Q5. (a) Show that the curl of F is the vector fieldVxF=i-j-k(b) Find a vector n (with positive z-component) normal to the surface o, in terms ofu, .(c) Find the total flux of VXF across the surface o, via direct evaluation; i.e. calculatethe integral(V x F). ds. Q6. (a) Show that the curve I(t) defined by the intersection between the surface o and thecylinder x² + y² = 1, and parametrised by t € [0, 2π] can be written asr(t) = (cost, sint, 1)(b) Find the path integral of the vector field F along the path I'(t)SF.dr(c) State the theorem that relates the answers to Q5 (c) and Q6(b), and explain howthis enables an interpretation of the curl of a vector field

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Answered: Q5. (a) Show that the curl of F is the…

Math

Trigonometry

Q5. (a) Show that the curl of F is the vector field VxF=i-j-k

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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Q5. (a) Show that the curl of F is the vector field
VxF=i-j-k
(b) Find a vector n (with positive z-component) normal to the surface o, in terms of
u, .
(c) Find the total flux of VXF across the surface o, via direct evaluation; i.e. calculate
the integral
(V x F). ds.

Q6. (a) Show that the curve I(t) defined by the intersection between the surface o and the
cylinder x² + y² = 1, and parametrised by t € [0, 2π] can be written as
r(t) = (cost, sint, 1)
(b) Find the path integral of the vector field F along the path I'(t)
S
F.dr
(c) State the theorem that relates the answers to Q5 (c) and Q6(b), and explain how
this enables an interpretation of the curl of a vector field

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